On the representation of measures over bounded lattices

In this paper we investigate measures over bounded lattices, extending and giving a unifying treatment to previous works. In particular, we prove that the measures of an arbitrary bounded lattice can be represented as measures over a suitably chosen Boolean lattice. Using techniques from algebraic g...

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Detalles Bibliográficos
Autores: Massri, Cesar Dario, Holik, Federico Hernán
Tipo de recurso: artículo
Estado:Versión publicada
Fecha de publicación:2021
País:Argentina
Institución:Consejo Nacional de Investigaciones Científicas y Técnicas
Repositorio:CONICET Digital (CONICET)
Idioma:inglés
OAI Identifier:oai:ri.conicet.gov.ar:11336/181158
Acceso en línea:http://hdl.handle.net/11336/181158
Access Level:acceso abierto
Palabra clave:LATTICES
MEASURABILITY
MEASURE FUNCTOR
REPRESENTABILITY
https://purl.org/becyt/ford/1.1
https://purl.org/becyt/ford/1
Descripción
Sumario:In this paper we investigate measures over bounded lattices, extending and giving a unifying treatment to previous works. In particular, we prove that the measures of an arbitrary bounded lattice can be represented as measures over a suitably chosen Boolean lattice. Using techniques from algebraic geometry, we also prove that given a bounded lattice X there exists a scheme X such that a measure over X is the same as a (scheme-theoretic) measure over X. We also define the measurability of a lattice, and describe measures over finite lattices.